Problem: Solve for $x$. $2x^2 - 28x + 98 = 0$ $x = $
Solution: Dividing both sides by $2$ gives: $ x^2 {-14}x + {49} = 0 $ The coefficient on the $x$ term is $-14$ and the constant term is $49$, so we need to find two numbers that add up to $-14$ and multiply to $49$. The number $-7$ used twice satisfies both conditions: $ {-7} + {-7} = {-14} $ $ {-7} \times {-7} = {49} $ So $(x - {7})^2 = 0$. $x - 7 = 0$ Thus, $x = 7$ is the solution.